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          <h1 class="post-title" itemprop="name headline">信息论中对于定长编码和哈夫曼编码效率的比较
              
            
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        <p>这是期末信息论课程的一次实验内容，实验进行了定长和哈夫曼码的编码和译码，同时也比较了两种编码的编码效率，比较有意思。</p>
<h3 id="实验内容："><a href="#实验内容：" class="headerlink" title="实验内容："></a>实验内容：</h3><p>掷骰子游戏，每次同时抛掷两枚骰子，将两枚骰子点数的和作为游戏的结果，重复抛掷 1000 次（视为 1000 次信源符号输出）。 要求： (1) 对 1000 次游戏结果进行逐符号二进制定长编码和译码。 (2) 对 1000 次游戏结果进行逐符号二进制变长编码和译码（Huffman 编码） 。 (3) 比较上述两种编码的效率。</p>
<h3 id="解决方案："><a href="#解决方案：" class="headerlink" title="解决方案："></a>解决方案：</h3><p>#Theory of Information extra section</p>
<p>#Author:Jason Bian</p>
<p>import random<br>import math</p>
<p>#set the max_range<br>max_range=1000</p>
<p>#get random numbers with two dices<br>dice_arr=[]<br>for i in range(0,max_range):<br>    tempdice1=random.randint(1,6)<br>    tempdice2=random.randint(1,6)<br>    tempdicetotal=tempdice1+tempdice2<br>    dice_arr.append(tempdicetotal)<br>print “dicrArray is “,dice_arr</p>
<p>#define fixed encoding code<br>fixedEncoding_arr={2:”0000”,3:”0001”,4:”0010”,5:”0011”,6:”0100”,7:”0101”,8:”0110”,9:”0111”,10:”1000”,11:”1001”,12:”1010”}</p>
<p>#use random numbers generate fixed code<br>fixedArray=[]<br>for i in range(len(dice_arr)):<br>    fixedArray.append(fixedEncoding_arr[dice_arr[i]])<br>print “fixedArray is “,fixedArray<br>fixedCode=””.join(fixedArray)<br>print “fixedCode is “,fixedCode</p>
<p>#collect char freqs<br>freqs_arr={2:0,3:0,4:0,5:0,6:0,7:0,8:0,9:0,10:0,11:0,12:0}<br>for i in range(len(dice_arr)):<br>    freqs_arr[dice_arr[i]]+=1<br>print “fixed code freqsArray is “,freqs_arr</p>
<p>#calc the probability of each code<br>prob_arr=[]<br>for i in freqs_arr:<br>    prob_arr.append(float(freqs_arr[i])/float(max_range))<br>print “code probability arr is “,prob_arr</p>
<p>#calc the information entropy<br>informationEntropy=0.0<br>for i in range(len(prob_arr)):<br>    if prob_arr[i]!=0:<br>        informationEntropy=informationEntropy-prob_arr[i]*math.log(prob_arr[i],2)<br>print “information entropy is “,informationEntropy</p>
<p>#print fixed code table<br>print “fixed Code Table:”<br>for i in freqs_arr:<br>    print “Number:%s  freq:%-2d  encoding: %s”%(i,freqs_arr[i],fixedEncoding_arr[i])</p>
<p>#calc the fixed code efficiency<br>fixedEffic=(max_range*informationEntropy)/(4*max_range*math.log(2,2))<br>print “fixed code efficiency is “,fixedEffic</p>
<p>#decode the fixed code<br>lPos=0<br>rPos=4<br>fixedDecode=[]<br>for i in range(max_range):<br>    tempCode=fixedCode[lPos:rPos]<br>    for j in fixedEncoding_arr:<br>        if fixedEncoding_arr[j]==tempCode:<br>            fixedDecode.append(j)<br>    lPos=lPos+4<br>    rPos=rPos+4<br>print “the decode of fixed code is “,fixedDecode</p>
<p>#Huffman Tree-Node Type<br>class Node:<br>    def __init__(self,freq):<br>        self.left=None<br>        self.right=None<br>        self.father=None<br>        self.freq=freq<br>        def isLeft(self):<br>        return self.father.left==self</p>
<p>#create Huffman leaf node<br>def createNodes(freqs):<br>    return [Node(freq) for freq in freqs]</p>
<p>#create Huffman-Tree<br>def createHuffmanTree(nodes):<br>    queue=nodes[:]<br>    while len(queue)&gt;1:<br>        queue.sort(key=lambda item:item.freq)<br>        node_left=queue.pop(0)<br>        node_right=queue.pop(0)<br>        node_father=Node(node_left.freq+node_right.freq)<br>        node_father.left=node_left<br>        node_father.right=node_right<br>        node_left.father=node_father<br>        node_right.father=node_father<br>        queue.append(node_father)<br>    queue[0].father=None<br>    return queue[0]</p>
<p>#Huffman Encoding<br>def huffmanEncoding(nodes,root):<br>    codes=[‘’]*len(nodes)<br>    for i in range(len(nodes)):<br>        node_tmp=nodes[i]<br>        while node_tmp!=root:<br>            if node_tmp.isLeft():<br>                codes[i]=’0’+codes[i]<br>            else:<br>                codes[i]=’1’+codes[i]<br>            node_tmp=node_tmp.father<br>    return codes</p>
<p>#generate Huffman Tree<br>nodes=createNodes(freqs_arr[i] for i in freqs_arr)<br>root=createHuffmanTree(nodes)<br>HuffmanCodes=huffmanEncoding(nodes,root)<br>print “HuffmanCodeArray is “,HuffmanCodes</p>
<p>#print Huffman Code Table<br>temp_range=0<br>print “Huffman Code Table:”<br>for i in freqs_arr:<br>    print “Number:%s  freq:%-2d  encoding: %s”%(i,freqs_arr[i],HuffmanCodes[temp_range])<br>    temp_range=temp_range+1</p>
<p>#use random numbers generate Huffman code<br>HuffmanArray=[]<br>for i in range(len(dice_arr)):<br>    HuffmanArray.append(HuffmanCodes[dice_arr[i]-2])<br>print “HuffmanArray is “,HuffmanArray<br>HuffmanCode=””.join(HuffmanArray)<br>print “HuffmanCode is “,HuffmanCode</p>
<p>#calc the Huffman average code length<br>HuffmanAveLen=0<br>for i in range(len(prob_arr)):<br>    HuffmanAveLen=HuffmanAveLen+prob_arr[i]*len(HuffmanCodes[i])<br>print “Huffman average length is “,HuffmanAveLen</p>
<p>#calc the Huffman code efficiency<br>HuffmanEffic=informationEntropy/(HuffmanAveLen*math.log(2,2))<br>print “Huffman code efficiency is “,HuffmanEffic</p>
<p>#decode the Huffman code<br>lPos=0<br>rPos=0<br>HuffmanDecode=[]<br>while(len(HuffmanDecode)&lt;max_range):<br>    tempCode=HuffmanCode[lPos:rPos]<br>    haveHuffman=0<br>    while(haveHuffman==0):<br>        rPos=rPos+1<br>        for j in range(len(HuffmanCodes)):<br>            if HuffmanCodes[j]==tempCode:<br>                HuffmanDecode.append(j+2)<br>                haveHuffman=1<br>        tempCode=HuffmanCode[lPos:rPos]<br>    lPos=rPos-1<br>    rPos=lPos+1<br>print “the decode of Huffman code is “,HuffmanDecode</p>
<p>raw_input(“press any key to quit”)</p>
<h3 id="用到的公式"><a href="#用到的公式" class="headerlink" title="用到的公式"></a>用到的公式</h3><p><a href="http://www.zhengzi.me/wordpress/wp-content/uploads/2016/01/无标题.png" target="_blank" rel="noopener"><img src="http://www.zhengzi.me/wordpress/wp-content/uploads/2016/01/无标题-300x246.png" alt="无标题"></a></p>

      
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